And subtract from it the 9th term (8 plus 1), which is 1171875
The difference is -1171872
Then divide by 1 minus the common ratio (5), so 1-5=-4
We get a quotient of 292968
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No offense to Bob, there is nothing intrinsically wrong with using Brute force. Its just a "less educated" way of doing it - its important to develop more analytical methods in order to pave the way for more difficult problems. You wouldnt want to use brute force if there were a hundred or a thousand terms, would you? What if there were an infinite number of terms?
In addition, you are more likely to make errors. There are too many numbers floating around, too many independent computations... there is a higher probability of making arithmetic or transcription errors. Notice Bob's seventh term is incorrect. He dyslexified two digits, placing his answer 180 higher than the true sum. And only with a measly 8 term series.
Answers & Comments
Verified answer
The sum of the geometric sequence
3, 15, 75, … if there are 8 terms is 292,958.
The 8th term is 234375.
The sum of the first eight terms is 292,968.
Bob B's answer needs correction as follows:
3 + 15 + 75 + 375 + 1875 + 9375 + 46875 + 234375 = 292,968
(Note: 48675 is wrongly added instead of 46875,
boosting the total by 1800).
292968
What you do is you take the first term 3
And subtract from it the 9th term (8 plus 1), which is 1171875
The difference is -1171872
Then divide by 1 minus the common ratio (5), so 1-5=-4
We get a quotient of 292968
======
No offense to Bob, there is nothing intrinsically wrong with using Brute force. Its just a "less educated" way of doing it - its important to develop more analytical methods in order to pave the way for more difficult problems. You wouldnt want to use brute force if there were a hundred or a thousand terms, would you? What if there were an infinite number of terms?
In addition, you are more likely to make errors. There are too many numbers floating around, too many independent computations... there is a higher probability of making arithmetic or transcription errors. Notice Bob's seventh term is incorrect. He dyslexified two digits, placing his answer 180 higher than the true sum. And only with a measly 8 term series.
For such a small number of terms, there's nothing wrong with using the brute force method.
Since each term is 5 times the previous term, calculate the remaining five terms and add them:
3 + 15 + 75 + 375 + 1875 + 9375 + 48675 + 234375 = 294,768
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There's a formula at the link below.